Question

form a quadratic polynomial for which zeroes are half the zeroes of x2 - 7x + 10

Answer 1

=x^2-5x-2x+10
=x (x-5)-2 (x-5)
(x-2)(x-7)
x=2and x=7

Answer 2

Let

p(x)=x2+7x+10

comparing with p(x)=ax2+bx+c

a=1,b=7,c=10

p(x)=x2+7x+10

⇒x2+5x+2x+10

⇒x(x+5)+2(x+5)

⇒(x+2)(x+5)

Let p(x)=0

⇒(x+2)(x+5)=0

x=−2,5

α=−2,β=−5

a−b=α+β⇒1−(7)=−7

ac=α⋅β⇒110=10